A gate is held in the position shown by cable AB. If the tension in the cable is 7.10 kN, determine the moment Mo made by the tension (as applied to point A) about the pivot point O of the gate. B 0.17 m A 6.7 m 6.1 m 0658 0.16 m 2.1 m Answer: Mo = i i+ i j+ i k)kN-m
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- The top of the folding workbench has a mass of 36 kg with mass center at G. Calculate the magnitude of the force supported by the pin at E. 225 mm D G Answers: E = F E 670 mm 1000 mm H i N B 805 mmA beam resting on two pivots has a length of L = 6.00 m and mass M = 77.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot placed a distance ℓ = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 61.5 kg steps onto the left end of the beam and begins walking to the right as in the figure below. The goal is to find the woman's position when the beam begins to tip. (a) Use the force equation of equilibrium to find the value of n2 when the beam is about to tip. (b) Using the result of part (c) and the torque equilibrium equation, with torques computed around the second pivot point, find the woman's position when the beam is about to tip.x = (c) Check the answer to part (e) by computing torques around the first pivot point.x = (d)Except for possible slight differences due to rounding, is the answer the same for F and E?L = 2.0 m A diver with a mass of 43 kg is standing 1.3 m from the left end of a diving board. This diving board has a mass of 83 kg and a length of 2 meters. It is supported by a pillar that is 0.5 m from the left end (labeled F, in the figure) and a bolt that holds the left end down (labeled F2 in the figure). What is the magnitude of the force from the pillar, labeled F1. F = What is the magnitude of the force from the end of the board, labeled F2. F2 = What position could the diver stand at to make both F, and F2 a minimum? 3:45 PM
- Review Conceptual Example 7 before starting this problem. A uniform plank of length 5.0 m and weight 225 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 375 N walk on the overhanging part of the plank before it just begins to tip? X = i 41.1 m²8.+ A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force N, and a frictional forcef, on the ladder. However, since the wall is frictionless, it exerts only a normal force N₂ on the ladder. The ladder has a length of L = 4.2 m, a weight of W, = 66.5 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m= 90 kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N₂ N₂- 4- (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N₂ N₂ Additional Materials
- A 9 m long board that has a mass of 14. Each end is held up by a vertical rope. A 45 kg box sits 1 m from the left end. Find the tension in the rope on the right. Hint: With forces applied at different places, this is a beam problem pick a pivot point measure all distances from the pivot point Apply Στ = 0 Don't forget torque = force x dist, so you need to multiply the masses by g = 9.8 m/s2 If you need more information, apply ΣF = 06